Omnipotence paradox
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The omnipotence paradox is a paradox arising from the attempt to apply logic to the notion of an omnipotent being. It appears when one asks whether or not an omnipotent being is able to limit its own omnipotence, thus becoming non-omnipotent. Some philosophers see it as proof of the impossibility of the existence of any such entity; others assert that the paradox arises from a misunderstanding or mischaracterization of the concept of omnipotence. In addition, several philosophers have considered the assumption that a being is either omnipotent or non-omnipotent to be a false dilemma, as it avoids the possibility of varying degrees of omnipotence (Haeckel).
The paradox is often based on the God of the Abrahamic religions, though this is not a requirement. Since the Middle Ages, philosophers have phrased the paradox in many ways, of which the classic example is, "Could an omnipotent being create a stone so heavy that even that being could not lift it?" This particular statement has subtle flaws (discussed below), but as the most famous version, it still serves adequately for illustrating the different ways the paradox has been analyzed.
In order to analyse the omnipotence paradox in a rigorous way, one must first establish the precise definition of omnipotence. The definition of omnipotence varies amongst cultures and religions, and from one philosopher to another. A common definition is "all-powerful", but that is insufficient for the omnipotence paradox. This paradox cannot be formulated, for example, if one defines omnipotence as the ability to operate outside the constraints of any logical framework. Modern approaches to the problem have involved the study of semantics, debating whether language—and therefore philosophy—can meaningfully address the concept of omnipotence itself.
Philosophical responses
A common example of the omnipotence paradox is expressed in the question, "Could an omnipotent being create a stone that it could not lift?" It is possible to analyze this question in the following manner:
- The being can either create a stone which it cannot lift, or it cannot create a stone which it cannot lift.
- If the being can create a stone which it cannot lift, then it is not omnipotent.
- If the being cannot create a stone which it cannot lift, then it is not omnipotent.
This mirrors the solution to another classic paradox, the irresistible force paradox: What happens when an irresistible force meets an immovable object? A response to this paradox is that if a force is irresistible, then by definition there is no truly immovable object; conversely, if an immovable object were to exist, then no force could be defined as being truly irresistible. This treatment of the paradox remains true to the basic assertions, but does not address the issue of the definition of omnipotence. Furthermore, the omnipotence paradox is related to another similar philosophical question, the grandfather paradox: Would it be possible to go back in time and kill one's own grandfather and thus never exist?. The vernacular definition of omnipotence often seems to include the ability to travel across time; one could then ask the question, "Can an omnipotent being go back in time and kill his own grandfather?" This is not, however, a logically satisfactory analysis of the paradox, as it tends to focus on the imposition of human attributes onto a being that is not necessarily of human form (Wierenga).
One can also attempt to resolve the paradox by postulating that omnipotence does not necessarily demand that a being must be able to do all things at all times. Thus, one reasons,
- The being can create a stone which it cannot at that moment lift.
- However, being omnipotent, the being can always later reduce the weight of the stone or give itself additional strength, so that it will be able to lift it. Therefore the being is still legitimately omnipotent.
This is essentially the same view espoused by Matthew Harrison Brady, a character in Inherit the Wind loosely based upon William Jennings Bryan. In the climactic scene of the 1960 movie version, Brady argues, "Natural law was born in the mind of the Creator. He can change it—cancel it—use it as He pleases!" Changing a stone's weight is logically equivalent to changing the effect of gravity. A slight variation of this view is central to the Christian faith. In the Christian gospels an omnipotent creator voluntarily empties himself of a portion of his power and enters his own creation. In this scenario the omnipotent being is (to some extent) limited by the laws of his own created universe. Upon exiting his creation the being reclaims his unlimited power. Given this reasoning, one can debate the definition of omnipotence yet again: can an omnipotent being create a stone so immutable that the being itself cannot reduce the stone's weight? Furthermore, does this situation impose a requirement on the omnipotent being—i.e., that it later reduce the stone's weight—thereby limiting the omnipotent being's free will?
The classic statement of the "irresistible force" paradox suffers from shortcomings when viewed in the context of modern physics, for a cannonball which cannot be deflected and a wall which cannot be knocked down are both objects of the same impossible type, that is, objects of infinite inertia. However, this is a statement of physics, which does not directly address the logic of the paradox; it only influences the choice of philosophical examples that we use to illustrate it. Likewise, the classic statement of the omnipotence paradox—a rock so heavy that its omnipotent creator cannot lift it—is grounded in Aristotelian science. This statement assumes both a geocentric cosmos and a flat Earth—can a stone only be "lifted" relative to the surface of the planet? Furthermore, if one considers the stone's position relative to the sun around which the planet orbits, one could hold that the stone is constantly being lifted. Pedantically speaking, modern physics indicates that the choice of phrasing about lifting stones may be a poor one; however, this does not in itself invalidate the fundamental concept of the generalized omnipotence paradox. Following Stephen Hawking's contemplations of the relation between a creator deity and natural law, one might modify the classic statement as follows:
- An omnipotent being creates a universe which follows the laws of Aristotelian physics.
- Within this universe, can the omnipotent being create a stone so heavy that the being cannot lift it?
Science writer James Gleick, in his biography of Richard Feynman, observes that the paradox arose when scientists began to debate the existence of atoms: could an omnipotent being — in this case, assumed to be the Christian God — create atoms that he himself could not split?
Upon basic consideration, the omnipotence paradox is conceptually identical to the observation that tolerant societies are intolerant towards intolerance, because were the society to tolerate intolerance, it would itself be an intolerant society. Similarly, when God is described as being omnipotent, this description must be understood to exclude any activities which would undermine such perfection. God's inability to die, for example, does not jeopardise his omnipotence but bolsters it. So the paradox may be resolved by introducing the caveat that God is bound by his own perfection and as such would be unable to create a stone so heavy that he could not lift it. Whether or not this can still be termed omnipotence is now reduced solely to a question of semantics.
Essential Omnipotence
If a being is essentially omnipotent, then it can resolve the paradox:
- The omnipotent being is essentially omnipotent, and therefore it is impossible for it to be non-omnipotent.
- Furthermore, the omnipotent being cannot do what is logically impossible.
- Creation of a stone which the omnipotent being cannot lift would be an impossibility, ergo the omnipotent being is not required to do such a thing.
- The omnipotent being cannot create such a stone, but nevertheless retains its omnipotence.
This necessarily accepts the view that even an omnipotent being cannot violate the laws of logic, and indeed this whole paradox can be seen as a strong reason for such a view. The philosopher Averroës advanced the omnipotence paradox for this reason (for which he was condemned by Bishop Tempier), although instead of phrasing it in terms of stones, he asked whether God could create a triangle with internal angles that did not add up to 180 degrees.
Note that the later discovery of non-Euclidean geometry does not resolve this question; for one might as well ask, "If given the axioms of Riemannian geometry, can an omnipotent being create a triangle whose angles do not add up to more than 180 degrees?" In either case, the real question is whether or not an omnipotent being would have the ability to evade the consequences which follow logically from a system of axioms that the being created.
The philosopher Nicholas Everitt, however, invites us to consider a 'nullipotent', a being for whom it is logically impossible to do anything. Taking the view that an omnipotent being cannot do what is logically impossible, then, the nullipotent has to be considered an omnipotent being.
For an overview of this formulation and the historical context in which it emerged, see James Burke's The Day the Universe Changed, either the second episode of the television series or the second chapter of the companion book. After the Reconquista, translations of Arab scientific and philosophical works—many of them in turn translations of Ancient Greek material—entered European intellectual society. When Averroës's conundrum reached Paris, it became part of a controversy which led to the University's theology students going on strike for six years. As Burke phrases the matter, "This 'limitations on God' stuff was dyhttp://dictionary.com/namite."
Mainstream Catholic theology eventually reconciled itself to the Greek and Arabic material the Reconquista made available, thanks in large part to Thomas Aquinas, whose Summa Theologica affirmed the notion that God could not defy logic. In this respect, Aquinas follows the thinking of Maimonides, the twelfth-century Jewish philosopher and physician, who makes the same proposition in his Guide for the Perplexed. Maimonides was an adherent of negative theology, a discipline which holds that one can only describe God via negations. A somewhat mystical view, negative or "Apophatic" theology centers upon the concept that God's true essence cannot be spoken, and that all affirmative descriptions of God risk being blasphemous or heretical.
Ethan Allen, a combatant in the American Revolution, wrote a treatise entitled Reason: The Only Oracle of Man, which addresses the topics of original sin, theodicy and several others in classic Enlightenment fashion. In Chapter 3, section IV, he notes that "omnipotence itself" could not exempt animal life from mortality, since change and death are defining attributes of such life. He argues, "the one cannot be without the other, any more than there could be a compact number of mountains without valleys, or that I could exist and not exist at the same time, or that God should effect any other contradiction in nature." Labeled by his friends a Deist, Allen accepted the notion of a divine being, though throughout Reason he argues that even a divine being must be circumscribed by logic.
The statement "God is infallible but can he find fallibility in himself" is innately false. If God is infallible than why would he have a need to find flaws within himself. Essentially there would be no flaws to find, enabling God to preserve his omnipotence while still not being able to perform an action. This statement is comparable to other omnipotence paradoxes in that one statement must be false. For example, in the paradox "can God create a stone which he himself cannot lift" either God has no need for such a situation to arise or there is no such thing as omnipotence to begin with, only omnipotence as a means of comparison. God is omnipotent to humans but whose to say that even God doesn't idolize a God of his own. Human comprehension of omnipotence might in fact be extrememly limited. Our basic understanding of "limitless" power might just be the tip of the iceberg.
Logically impossible
Some philosophers maintain that the paradox can be resolved if the definition of omnipotence includes Descartes' view that an omnipotent being can do the logically impossible:
- An omnipotent being can do the logically impossible.
- The omnipotent being creates a stone which it cannot lift.
- The omnipotent being then lifts the stone.
Presumably, such a being could also make the sum 2 + 2 = 5 become mathematically possible, or could create a square circle. In the words of Harry Frankfurt, "If an omnipotent being can do what is logically impossible, then he can not only create situations which he cannot handle but also, since he is not bound by the limits of consistency, he can handle situations which he cannot handle."
However, this attempt to resolve the paradox is problematic in that the definition itself forgoes logical consistency. The paradox may be solved, but at the expense of rendering logic futile, unnecessary or meaningless in defining such a being since such a being transcends logic.
Pop culture and humorous responses
The omnipotence paradox has infiltrated popular culture. References to the omnipotence paradox and similar debates such as the existence of an omnipotent being can be found in a variety of media.
- Stephen Hawking's A Brief History of Time introduces the omnipotence paradox within a more general discussion of what role a creator deity might play in relation to natural laws. In a later book, Black Holes and Baby Universes, Hawking notes half-jokingly that including these religious speculations—including the book's last line, "for then we would know the mind of God"—probably doubled A Brief History's sales.
- The modern science of quantum mechanics postulates that all material objects naturally exist in a superposition of states. Though the basic equations of quantum mechanics can be interpreted in several different ways, a common viewpoint states that when an object is observed or measured, it "collapses" into a single state. The solution of the Schrödinger equation expresses the probability that a particle will collapse into a particular quantum state. This concept has led to a tongue-in-cheek solution for the omnipotence paradox, in the tradition of physicist humor exemplified by Schrödinger's cat. An omnipotent being could prevent others from observing it. Such a being could then both create a stone it cannot lift and lift the stone at the same time, and because others could not observe it doing so, there would be no way to confirm the outcome of events. Greg Egan's novel Quarantine explores some of these issues in a fictional context.
- Peter Suber discusses the paradox of legal omnipotence—defined as the ability of a legal system to make any law at any time—in The Paradox of Self-Amendment: A Study of Law, Logic, Omnipotence, and Change, taking up such questions as how a legal system can amend itself, and whether an omnipotent legal system can terminate its own omnipotence. Suber created the game Nomic in part to explore such questions.
- In an episode of The Simpsons (season 13, episode 285), Homer Simpson asks Ned Flanders, "Could Jesus microwave a burrito so hot that He Himself could not eat it?"
- In the Star Trek universe the entity known as "Q" is omnipotent and many of the above discussions are addressed, typically in a humorous vein. See the "Q" Episodes section for specific episodes dealing with the issues of omnipotence.
References
- External links in the following were last verified 16 November 2005.
- Haeckel, Ernst. The Riddle of the Universe. Harper and Brothers, 1900.
- Hoffman, Joshua, Rosenkrantz, Gary. "Omnipotence" The Stanford Encyclopedia of Philosophy (Summer 2002 Edition). Edward N. Zalta (ed.)
- Wierenga, Edward. "Omnipotence" The Nature of God: An Inquiry into Divine Attributes. Cornell University Press, 1989.
- Gleick, James. Genius. Pantheon, 1992. ISBN 0-679-40836-3.
- Burke, James. The Day the Universe Changed. Little, Brown; 1995 (paperback edition). ISBN 0-316-11704-8.
- Allen, Ethan. Reason: The Only Oracle of Man. J.P. Mendum, Cornill; 1854. Originally published 1784, available online.